The Uncertainty Principle

Abstract

It has thus far been assumed that the received signal is reflected from a stationary target so that the carrier frequency of the transmitted and reflected signals coincide. The general case will now be considered. Assume that the signal is reflected from a target whose range is r0, and whose range rate is v0. Thus the reflected signal is delayed by the time t0 = 2r0/c and acquires a Doppler shift of Q = (2v0/c) ω0: